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library(readxl)
library(tidyverse)
library(patchwork)
library(hrbrthemes)
library(DT)
library(knitr)
library(plotly)
library(tidyr)
library(dplyr)
library(car)
library(lme4)
library(lmerTest)
library(easystats)1 Analysis of the Satiety Questionnaire
1.1 Load Libraries
1.2 Load Satiety Data
Data is displayed in wide format - each participant has a row - Column format is Intervention_Question_Time format (e.g. HUEL_S1_0 and Cornflakes_S6_180). I currently have not included AP009 as they pulled out, will discuss with Matt
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# Read the cleaned Satiety Study
Satiety <- read_excel("../Input/HUEL_satiety_input.xlsx")
#load function
source(file = "../R/HUEL_satiety_functions.R")
# Create an interactive table
datatable(Satiety, filter = "top")Lets convert to long format - this won’t need repeating on the subsequent analysis
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# create a long format
Satiety_long <- Satiety %>%
pivot_longer(cols = starts_with("HUEL_") | starts_with("Cornflakes_"), names_to = "Timepoint", values_to = "Measurement")
# Create Intervention column based on Timepoint
Satiety_long <- Satiety_long %>%
mutate(Intervention = ifelse(str_detect(Timepoint, "^HUEL"), "HUEL", "Cornflakes"),
Timepoint = gsub("^HUEL_|^Cornflakes_", "", Timepoint),
Question = gsub("_.*", "", Timepoint),
Timepoint = gsub("^S\\d+_", "", Timepoint))2 Q1.
First subset the question:
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#Subset the question
S1_subset_data <- subset_data(Satiety_long, "S1")Then mean +- SD and a graph:
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# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S1 <- calculate_mean_sd(Satiety_long, question = "S1")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
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plot <- plot_mean_sd(result_S1)
print(plot)
2.1 2 Way ANOVA and Checking the assumptions
Then running functions to create and check a 2 way ANOVA (Intervention (HUEL or Cornflakes), Timepoint (0 to 240 minute) and Interaction (Intervention x Timepoint)) and a Mixed effects model (Intervention (HUEL or Cornflakes), Timepoint (0 to 240 minute) and Interaction (Intervention x Timepoint), with random effect of participant
Unsure whether to do in the mixed effects model:
(1 | participant) includes random intercepts for participants, capturing individual differences in baseline hunger levels. or (1 | participant:time) includes random intercepts for the interaction between participants and time, capturing variability in hunger ratings across different time points within each participant. .
Then a 2 way ANOVA and assumptions
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#| layout-ncol: 2
S1_anova_results_with_plots <- two_way_anova_with_plots(S1_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 1.1252 0.3146
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 16945 16945 34.540 6.03e-09 ***
Timepoint 10 210890 21089 42.986 < 2e-16 ***
Intervention:Timepoint 10 1886 189 0.384 0.954
Residuals 836 410144 491
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 2.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
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S1_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S1_subset_data)
anova(S1_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 210890 21089.0 10 798 87.219 < 2.2e-16 ***
Intervention 16945 16945.2 1 798 70.081 2.54e-16 ***
Timepoint:Intervention 1886 188.6 10 798 0.780 0.6482
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S1_lmer_model)
Looks like the data will need to be transformed….
3 Q2.
First subset the question:
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#Subset the question
S2_subset_data <- subset_data(Satiety_long, "S2")means and graph
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# create mean +- SD table for HUEL and Cornflakes S2, 0 to 240 minutes
result_S2 <- calculate_mean_sd(Satiety_long, question = "S2")
kable(result_S2)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 26.2 | 21.7 | 21.4 | 15.2 |
| 15 | 63.4 | 69.3 | 27.2 | 26.2 |
| 30 | 64.0 | 69.6 | 24.4 | 25.1 |
| 45 | 62.5 | 71.9 | 24.7 | 21.0 |
| 60 | 58.1 | 70.5 | 24.7 | 21.7 |
| 90 | 51.7 | 64.5 | 24.5 | 21.7 |
| 120 | 48.3 | 59.0 | 24.4 | 22.8 |
| 150 | 40.9 | 53.7 | 22.7 | 21.8 |
| 180 | 38.2 | 46.6 | 22.6 | 24.0 |
| 210 | 30.1 | 40.8 | 22.1 | 24.3 |
| 240 | 28.4 | 36.5 | 23.9 | 23.3 |
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plot <- plot_mean_sd(result_S2)
print(plot)
3.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
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#| layout-ncol: 2
S2_anova_results_with_plots <- two_way_anova_with_plots(S2_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 1.1758 0.2645
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 15080 15080 27.82 1.7e-07 ***
Timepoint 10 186194 18619 34.35 < 2e-16 ***
Intervention:Timepoint 10 4826 483 0.89 0.542
Residuals 836 453178 542
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 3.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
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S2_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S2_subset_data)
anova(S2_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 186194 18619.4 10 798 54.3725 < 2.2e-16 ***
Intervention 15080 15079.7 1 798 44.0359 5.949e-11 ***
Timepoint:Intervention 4826 482.6 10 798 1.4093 0.1712
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S2_lmer_model)
4 Q3
First subset the question:
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#Subset the question
S3_subset_data <- subset_data(Satiety_long, "S3")Then means and graph
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# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S3 <- calculate_mean_sd(Satiety_long, question = "S3")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
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plot <- plot_mean_sd(result_S3)
print(plot)
4.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S3_anova_results_with_plots <- two_way_anova_with_plots(S3_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 2.4863 0.0002463 ***
836
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 18741 18741 36.722 2.06e-09 ***
Timepoint 10 273983 27398 53.685 < 2e-16 ***
Intervention:Timepoint 10 2129 213 0.417 0.939
Residuals 836 426658 510
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 4.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S3_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S3_subset_data)
anova(S3_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 273983 27398.3 10 798 101.8963 < 2.2e-16 ***
Intervention 18741 18741.4 1 798 69.7005 3.034e-16 ***
Timepoint:Intervention 2129 212.9 10 798 0.7918 0.6368
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S3_lmer_model)
5 Q4
First subset the question:
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#Subset the question
S4_subset_data <- subset_data(Satiety_long, "S4")Mean and graph:
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# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S4 <- calculate_mean_sd(Satiety_long, question = "S4")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
Show the code
plot <- plot_mean_sd(result_S4)
print(plot)
5.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S4_anova_results_with_plots <- two_way_anova_with_plots(S4_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 0.7148 0.8206
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 13025 13025 22.755 2.17e-06 ***
Timepoint 10 156857 15686 27.403 < 2e-16 ***
Intervention:Timepoint 10 1671 167 0.292 0.983
Residuals 836 478532 572
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 5.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S4_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S4_subset_data)
anova(S4_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 156857 15685.7 10 798 53.0928 < 2.2e-16 ***
Intervention 13025 13025.2 1 798 44.0878 5.802e-11 ***
Timepoint:Intervention 1671 167.1 10 798 0.5656 0.8426
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S4_lmer_model)
6 Q5
First subset the question:
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#Subset the question
S5_subset_data <- subset_data(Satiety_long, "S5")Mean and graph
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# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S5 <- calculate_mean_sd(Satiety_long, question = "S5")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
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plot <- plot_mean_sd(result_S5)
print(plot)
6.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S5_anova_results_with_plots <- two_way_anova_with_plots(S5_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 0.756 0.775
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 11208 11208 16.636 4.96e-05 ***
Timepoint 10 41226 4123 6.119 4.83e-09 ***
Intervention:Timepoint 10 1747 175 0.259 0.989
Residuals 836 563216 674
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 6.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S5_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S5_subset_data)
anova(S5_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 41226 4122.6 10 798 14.7259 < 2.2e-16 ***
Intervention 11208 11207.7 1 798 40.0336 4.158e-10 ***
Timepoint:Intervention 1747 174.7 10 798 0.6239 0.7942
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S5_lmer_model)
7 Q6
Show the code
# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S6 <- calculate_mean_sd(Satiety_long, question = "S6")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
Show the code
plot <- plot_mean_sd(result_S6)
print(plot)
First subset the question:
Show the code
#Subset the question
S6_subset_data <- subset_data(Satiety_long, "S6")7.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S6_anova_results_with_plots <- two_way_anova_with_plots(S6_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 0.4653 0.9811
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 1312 1312 1.737 0.188
Timepoint 10 58479 5848 7.743 6.21e-12 ***
Intervention:Timepoint 10 1099 110 0.146 0.999
Residuals 836 631380 755
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 7.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S6_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S6_subset_data)
anova(S6_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 58479 5847.9 10 798 17.4081 < 2e-16 ***
Intervention 1312 1312.0 1 798 3.9056 0.04847 *
Timepoint:Intervention 1099 109.9 10 798 0.3272 0.97399
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S6_lmer_model)
8 Q7
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# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S7 <- calculate_mean_sd(Satiety_long, question = "S7")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
Show the code
plot <- plot_mean_sd(result_S7)
print(plot)
First subset the question:
Show the code
#Subset the question
S7_subset_data <- subset_data(Satiety_long, "S7")8.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S7_anova_results_with_plots <- two_way_anova_with_plots(S7_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 0.5328 0.9579
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 2840 2840 3.700 0.0548 .
Timepoint 10 107893 10789 14.055 <2e-16 ***
Intervention:Timepoint 10 1056 106 0.138 0.9993
Residuals 836 641764 768
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 8.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S7_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S7_subset_data)
anova(S7_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 107893 10789.3 10 798 32.0034 < 2.2e-16 ***
Intervention 2840 2840.0 1 798 8.4241 0.003805 **
Timepoint:Intervention 1056 105.6 10 798 0.3132 0.977899
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S7_lmer_model)
9 Q8
Show the code
# create mean +- SD table for HUEL and Cornflakes S1, 0 to 240 minutes
result_S8 <- calculate_mean_sd(Satiety_long, question = "S8")
kable(result_S1)| Timepoint | Mean_Cornflakes | Mean_HUEL | SD_Cornflakes | SD_HUEL |
|---|---|---|---|---|
| 0 | 62.3 | 60.5 | 20.0 | 21.9 |
| 15 | 26.3 | 21.5 | 22.4 | 21.4 |
| 30 | 31.1 | 18.7 | 26.1 | 17.2 |
| 45 | 31.6 | 21.4 | 24.1 | 19.4 |
| 60 | 34.7 | 24.3 | 24.0 | 19.9 |
| 90 | 37.8 | 28.9 | 22.5 | 21.8 |
| 120 | 45.2 | 34.9 | 23.2 | 22.6 |
| 150 | 52.5 | 40.3 | 22.3 | 23.4 |
| 180 | 60.0 | 51.0 | 21.7 | 25.0 |
| 210 | 65.5 | 56.3 | 20.0 | 25.6 |
| 240 | 72.4 | 63.8 | 18.2 | 22.0 |
Show the code
plot <- plot_mean_sd(result_S8)
print(plot)
First subset the question:
Show the code
#Subset the question
S8_subset_data <- subset_data(Satiety_long, "S8")9.1 2 Way ANOVA and Checking the assumptions
Then a 2 way ANOVA and assumptions
Show the code
#| layout-ncol: 2
S8_anova_results_with_plots <- two_way_anova_with_plots(S8_subset_data)Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 21 0.7087 0.827
836
NULL
Df Sum Sq Mean Sq F value Pr(>F)
Intervention 1 630 629.6 0.711 0.399268
Timepoint 10 28694 2869.4 3.241 0.000408 ***
Intervention:Timepoint 10 738 73.8 0.083 0.999924
Residuals 836 740059 885.2
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Independence of residuals: TRUE 9.2 linear mixed model and assumptions
And let’s try linear mixed model instead where we account for participants, as well as assumptions
Show the code
S8_lmer_model <- lmer(Measurement ~ Timepoint * Intervention + (1|Participant), data = S8_subset_data)
anova(S8_lmer_model)Type III Analysis of Variance Table with Satterthwaite's method
Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
Timepoint 28694.3 2869.43 10 798 14.0461 < 2e-16 ***
Intervention 629.6 629.63 1 798 3.0821 0.07954 .
Timepoint:Intervention 737.9 73.79 10 798 0.3612 0.96280
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Show the code
check_model(S8_lmer_model)